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Ben's Game

Age 11 to 14 Challenge Level:

Ben, Jack and Emma were playing a game with a box of $40$ counters - they were not using all of them.
They each had a small pile of counters in front of them.

Image of Ben, Jack and Emma with counters in front of them.

All at the same time, Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma, and Emma passed a fifth of her counters to Ben.

They all passed on more than one counter.

After this they all had the same number of counters.

How many could each of them have started with?



The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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